Regularization parameter selection in indirect regression by residual based bootstrap

TL;DR

This paper introduces a data-driven method for selecting regularization parameters in indirect regression using residual-based bootstrap, providing a uniform expansion and demonstrating its effectiveness through simulations.

Contribution

It develops a novel residual-based bootstrap technique for optimal regularization parameter selection in indirect regression models.

Findings

The method is asymptotically most precise.

Simulation studies confirm its effectiveness.

Provides a uniform expansion of the residual-based estimator.

Abstract

Residual-based analysis is generally considered a cornerstone of statistical methodology. For a special case of indirect regression, we investigate the residual-based empirical distribution function and provide a uniform expansion of this estimator, which is also shown to be asymptotically most precise. This investigation naturally leads to a completely data-driven technique for selecting a regularization parameter used in our indirect regression function estimator. The resulting methodology is based on a smooth bootstrap of the model residuals. A simulation study demonstrates the effectiveness of our approach.